A spring and block are in the arrangement of the figure below. When the block is

Question

A spring and block are in the arrangement of the figure below. When the block is pulled out to x = +5.0 cm, we must apply a force of magnitude 380 N to hold it there. We pull the block to x = +14.5 cm and then release it.

Figure (a): A spring in its relaxed state. The origin of an x axis has been placed at the end of the spring that is attached to a block. Figure (b): The block is displaced by d with arrow, and the spring is stretched by a positive amount x. Note the restoring force F with arrows exerted by the spring. Figure (c): The spring is compressed by a negative amount x. Again, note the restoring force.

For each of the following, find how much work the spring does on the block when the block moves from the first point given to the second point given the following

(a)    xi = 7.0 cm to x = 2.5 cm

b)    xi = 7.0 cm to x = -2.5 cm

(c)    xi = 7.0 cm to x = -7.0 cm

(d)    xi = 7.0 cm to x = -14.5 cm

Explanation / Answer

x = stretch in the spring = 5 cm = 0.05 m

Fs = spring force = 380 N

k = spring constant

using the formula

Fs = k x

380 = k (0.05)

k = 7600 N/m

a)

Work done by spring = change in spring potential energy = (0.5) k (Xf2 - Xi2) = (0.5) (7600) ((0.025)2 - (0.07)2)

W = - 16.25 J

b)

Work done by spring = change in spring potential energy = (0.5) k (Xf2 - Xi2) = (0.5) (7600) ((- 0.025)2 - (0.07)2)

W = - 16.25 J

c)

Work done by spring = change in spring potential energy = (0.5) k (Xf2 - Xi2) = (0.5) (7600) ((- 0.07)2 - (0.07)2)

W = 0 J

d)

Work done by spring = change in spring potential energy = (0.5) k (Xf2 - Xi2) = (0.5) (7600) ((- 0.145)2 - (0.07)2)

W = 61.275 J

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